ENGLISH ABSTRACT: In this thesis we study a wavelet construction procedure based on a multiresolutional
method, before specializing to the case of spline wavelets.
First, we introduce and analyze the concepts of scaling ...

In this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove ...

ENGLISH ABSTRACT: Subdivision is an important and e cient tool for rendering smooth curves and
surfaces in computer graphics, by repeatedly applying a subdivision (re ning)
scheme to a given set of points. In the literature, ...

De Wet, Wouter de Vos(Stellenbosch : University of Stellenbosch, 2007-12)

We study refinable functions where the dilation factor is not always assumed to be 2. In
our investigation, the role of convolutions and refinable step functions is emphasized as a
framework for understanding various ...

ENGLISH ABSTRACT: Multi-resolution analysis (MRA) has become a very popular eld of mathematical study
in the past two decades, being not only an area rich in applications but one that remains
lled with open problems. ...

Subdivision is an important iterative technique for the efficient generation of curves and
surfaces in geometric modelling. The convergence of a subdivision scheme is closely connected
to the existence of a corresponding ...

Subdivision techniques have, over the last two decades, developed into a powerful
tool in computer-aided geometric design (CAGD). In some applications it is
required that data be preserved exactly; hence the need for ...